Solvability of the system of equations of one-dimensional motion of a heat-conducting two-phase mixture. (English. Russian original) Zbl 1201.35003
Math. Notes 87, No. 2, 230-243 (2010); translation from Mat. Zametki 87, No. 2, 246-261 (2010).
Summary: We prove the local solvability of the initial boundary-value problem for the system of equations of one-dimensional nonstationary motion of a heat-conducting two-phase mixture (gas plus solid particles). For the case in which the real densities of the phases are constant, we establish the solvability “in the large” with respect to time.
MSC:
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
quasilinear system of equations; viscous gas; Lagrangian variable; Tikhonov-Schauder theorem; incompressible medium; local solvability; initial boundary-value problemReferences:
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